As you can see, I'm able to successfully draw the Lorenz attractor, before adding it the scene.

However, I can't animate the drawing of the attractor, by pushing new vertices onto the geometry within the render loop. Doing so causes the line not to be visible on screen. You can see where I've experimented with this approach in the commented out section of JavaScript from line 73 onwards.

Some searching has brought up the idea of using Three.js’s BufferGeometry class. However, I’m unclear as to what exactly that class does or how to apply it in this instance.